Best albums of 2012, No 4: Dirty Projectors – Swing Lo Magellan

Dirty Projectors … Now you can love as well as admire them. Photograph: Jason Frank Rothenberg

Over the years a viewpoint seems to have taken hold that Dirty Projectors are a band to admire rather than truly love. That their music represents some grand inside joke, rather than anything with an actual beating heart behind it. And that their fondness for, say, translating songs into the ancient script of Mesopotamia, the first non-pictographic written language as practised in 5,000BC between the Tigris and the Euphrates in the city of Ur, might possibly be considered a little pretentious.

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That some people were still trotting this line out after hearing the band's sixth album, Swing Lo Magellan, seems remarkable. Not just because the outlandish intellectual ideas here were matched with music that was so clearly warm, personal and of a striking beauty, but also because the closing song, Irresponsible Tune, explicitly stated the power of music perhaps more eloquently than anything else recorded this year. On that track, David Longstreth stretched his bafflingly elastic vocals around such simple yet poetic declarations as: "In my heart there is music, in my mind is a song/ But in my eyes, a world: crooked, fucked up and wrong." Funnily enough, the song itself sounded like a "crooked, fucked up and wrong" version of the Orioles' doo-wop hit Crying in the Chapel, but as an open-hearted love letter to the magic of music, it was up there with Lou Reed's Rock & Roll.

This being Dirty Projectors, you would hardly expect the rest of the album to be as concise or direct. There were, inevitably, impenetrable moments (the gruelling, guitar wrangle of Maybe That Was It) and, sure, an album named after a 16th-century Portuguese explorer was perhaps never going to appeal to those who buy their albums from Tesco. Yet it didn't take many repeat plays for Swing Lo Magellan to reveal its vast treasures: Amber Coffman's soulful lead vocal hooks on Socialites; the way the stripped back Just from Chevron deployed a brief yet devastatingly effective swell of strings; the breathtaking vocal climaxes of Coffman and Haley Dekle on the chorus of Gun Has No Trigger, a song that managed to question society's ability to enact dissent while also sounding like While My Guitar Gently Weeps (Longstreth's early love for the Beatles is frequently on display here).

Earlier this year, Longstreth told the Guardian his songs have always been personal, but this time the band weren't "hiding behind some obtuse conceptual frame". Given that past concepts have included covering Black Flag albums from memory and composing operas about the Eagles' Don Henley, it's no surprise this made Swing Lo Magellan the band's most accessible work to date. And whereas anyone who arrived here directly from Carly Rae Jepsen's Call Me Maybe might baulk at the idea that this was a pop record, the melodies were always strong and – thanks to their ability to ricochet off into the most unexpected places – frequently startling too. If you didn't "get" Dirty Projectors before, then Swing Lo Magellan was the album that opened the door a little to smooth your way in. And perhaps that's what made it the band's greatest triumph to date – that they could show off this magnificently, without ever really looking like they were showing off at all.